Question: Kevin works out for $\frac{5}{6}$ of an hour every day. To keep his exercise routines interesting, he includes different types of exercises, such as push-ups and sit-ups, in each workout. If each type of exercise takes $\frac{5}{18}$ of an hour, how many different types of exercise can Kevin do in each workout?
Solution: To find out how many types of exercise Kevin could do in each workout, divide the total amount of exercise time ( $\frac{5}{6}$ of an hour) by the amount of time each exercise type takes ( $\frac{5}{18}$ of an hour). $ \dfrac{{\dfrac{5}{6} \text{ hour}}} {{\dfrac{5}{18} \text{ hour per exercise}}} = {\text{ number of exercises}} $ Dividing by a fraction is the same as multiplying by the reciprocal. The reciprocal of ${\dfrac{5}{18} \text{ hour per exercise}}$ is ${\dfrac{18}{5} \text{ exercises per hour}}$ $ {\dfrac{5}{6}\text{ hour}} \times {\dfrac{18}{5} \text{ exercises per hour}} = {\text{ number of exercises}} $ $ \dfrac{{5} \cdot {18}} {{6} \cdot {5}} = {\text{ number of exercises}} $ Reduce terms with common factors by dividing the $5$ in the numerator and the $5$ in the denominator by $5$ $ \dfrac{{\cancel{5}^{1}} \cdot {18}} {{6} \cdot {\cancel{5}^{1}}} = {\text{ number of exercises}} $ Reduce terms with common factors by dividing the $18$ in the numerator and the $6$ in the denominator by $6$ $ \dfrac{{1} \cdot {\cancel{18}^{3}}} {{\cancel{6}^{1}} \cdot {1}} = {\text{ number of exercises}} $ Simplify: $ \dfrac{{1} \cdot {3}} {{1} \cdot {1}} = {3} $ Kevin can do 3 different types of exercise per workout.